Optical element and optical apparatus

ABSTRACT

An optical element includes an optical surface having a multilayer film. The multilayer film comprises a stack that includes a first film having a first refractive index for a used wavelength and a second film having a second refractive index for the used wavelength smaller than the first refractive index. Outermost layers of the stack are configured by the first films. A film configuration of the stack has symmetry along with a stack direction. The predetermined conditional expressions are satisfied.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to an optical element and an opticalapparatus.

Description of the Related Art

A thin film has been widely used in an optical element. The thin filmmeans a film having a thickness of about a wavelength of light or lessand adjusting optical functions using an interference effect of light.For example, to enhance a transmission quantity, an antireflection filmcancelling light waves is formed on an optical lens. Additionally, todivide light into reflected light and transmitted light for eachpolarization, a polarizing separation element increasing light waves isformed on a polarizing separation element. In Japanese Patent Laid-OpenNo. (“JP”) 2005-55543, to obtain desired characteristics, a polymeroptical multilayer film having stacked polymer thin films of which arefractive index and a thickness is appropriately selected is disclosed.

However, a conventional technology disclosed in JP 2005-55543 uses acommon material as the polymer thin films and thus is sensitive forwavelength characteristics and incident angle characteristics.

SUMMARY OF THE INVENTION

In view of the problem, it is an object of the present invention toprovide an optical element superior for wavelength characteristics andincident angle characteristics.

An optical element according to one aspect of the present inventionincludes an optical surface having a multilayer film. The multilayerfilm comprises a stack that includes a first film having a firstrefractive index for a used wavelength and a second film having a secondrefractive index for the used wavelength smaller than the firstrefractive index, outermost layers of the stack are configured by thefirst films, a film configuration of the stack has symmetry along with astack direction, and the following conditional expressions aresatisfied:

$\frac{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{M}^{2}\tan\;\Delta_{M}} - {U_{H}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}}{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{H}^{2}\tan\;\Delta_{M}} - {U_{M}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}} > 0$U_(H, M) = n_(H, M)cos   θ_(i)$\Delta_{{H,M}\;} = {\frac{2\;\pi}{\lambda_{i}}n_{H,M}d_{H,M}\cos\;\theta_{H,M}}$where λ_(i) is the used wavelength, θ_(i) is an incident angle of lightincident on the multilayer film, n_(H) is the first refractive index,n_(M) is the second refractive index, d_(H) is a physical thickness ofthe first film, and d_(M) is a physical thickness of the second film.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are schematic diagrams of an optical element accordingto embodiments of the present invention.

FIG. 2 is a chart illustrating reflectance characteristics of a SiO₂film.

FIG. 3 is a chart illustrating refractive index dispersion of a SiO₂film.

FIG. 4 is a chart illustrating refractive index dispersion of a Ta₂O₅film.

FIG. 5 is a chart illustrating an equivalent refractive index of anequivalent film (a first example).

FIG. 6 is a chart illustrating an equivalent physical thickness of theequivalent film (the first example).

FIG. 7 is a chart illustrating a calculation result of a conditionalexpression (4) (the first example).

FIG. 8 is a diagram illustrating an equivalent refractive index for awavelength of 550 nm (the first example).

FIG. 9 is a diagram illustrating a refractive index of wavelengths of400 to 700 nm (the first example).

FIG. 10 is a chart illustrating reflectance characteristics of adichroic film (the first example).

FIG. 11 is a chart illustrating an equivalent refractive index of anequivalent film (a second example).

FIG. 12 is a chart illustrating an equivalent physical thickness of theequivalent film (the second example).

FIG. 13 is a chart illustrating a calculation result of a conditionalexpression (4) (the second example).

FIG. 14 is a chart illustrating reflectance characteristics of anantireflection film (the second example).

FIG. 15 is a perspective view of a digital camera as one example of anoptical apparatus using an optical element of the present invention (athird example).

DESCRIPTION OF THE EMBODIMENTS

Exemplary embodiments of the present invention will be described belowwith reference to the accompanied drawings. In each of the drawings, thesame elements will be denoted by the same reference numerals and theduplicate descriptions thereof will be omitted.

FIGS. 1A and 1B are schematic diagrams of an optical element 100according to embodiments of the present invention. The optical element100 includes an optical surface that has a multilayer film formed on asubstrate 101. The multilayer film includes films 102 to 105. The films102 to 104 can use light interference. In general, a thin film usinglight interference has an optical thickness sufficiently smaller than aused wavelength, and optical thicknesses of the films 102 to 105 arealso within the above range. In this embodiment, a wavelength range ofincident light L1 will be explained as a visible range, but the otherwavelength range such as a near infrared wavelength may be used as theused wavelength range.

The films 102 to 104 are stacked in order from a substrate 101 side, andconfigure a film stack 106. The films 102 and 104 each have a firstrefractive index for the used wavelength, and the film 103 has a secondrefractive index for the used wavelength smaller than the firstrefractive index. In other words, the outermost layers of the film stack106 are configured by the films 102 and 104 having a higher refractiveindex. A film configuration of the film stack 106 also has symmetryalong with a stack direction. Accordingly, physical thicknesses of thefilms 102 and 104 are equivalent to each other.

If the film stack 106 includes at least two H-films (first films) havinga first refractive index and at least one M-film (a second film) havinga second refractive index smaller than the first refractive index, itsoutermost layers are configured by the H-film, and its filmconfiguration has symmetry along with a stacking direction, the filmstack 106 may have the other configuration. For example, the film stack106 may be configured by repeatedly stacking the films 102 to 104, andmay be configured to include films other than the films 102 to 104.

Nearly all materials of an interference thin film used for an opticalelement such as an optical lens have positive dispersion. The positivedispersion means that a refractive index increases with a smallerwavelength of light. Conversely, negative dispersion means that arefractive index decreases with a smaller wavelength of light. Ingeneral, when a wavelength of light shortens, in other words, afrequency increases, a transparent material has a higher refractiveindex by influence of polarization. Additionally, a dispersion quantitygenerally increases in proportion to an absolute value of a refractiveindex. A transparent material exceptionally has negative dispersion neara wavelength range where light is absorbed, but absorbs light at thesame time, thereby being difficult to use as an interference thin film.Moreover, a material of a metal is known to have negative dispersion,but is difficult to use as an interference thin film for the samereason.

In this embodiment, a multilayer film having negative dispersion isvirtually achieved on the basis of an interference thin film theory.Interference between lights reflected at upper and lower interfacesdetermines characteristics of the films 102 to 104. In interference oflight, amplitude of a wave and a phase of light are important. Ingeneral, the amplitude of a wave is calculated by a value referred to asa Fresnel coefficient r. When a reflective index of a film on anincident surface side for the used wavelength is n₀, a reflective indexof a film on an emitting surface side for the used wavelength is n₁, apropagation angle of light in the film on the incident surface side isθ₀, and a propagation angle of light in the film on the emitting surfaceside is θ₁, a Fresnel coefficient r_(s) of S polarization is expressedby the following expression (1). A Fresnel coefficient r_(p) of Ppolarization is also expressed by the following expression (2). In otherwords, the Fresnel coefficient r_(s) of S polarization is calculated asan amplitude ratio of an electric field, and the Fresnel coefficientr_(p) of P polarization is calculated as an amplitude ratio of amagnetic field.

$\begin{matrix}{r_{s} = {\frac{E_{rs}}{E_{is}} = \frac{{n_{0}\cos\;\theta_{0}} - {n_{1}\cos\;\theta_{1}}}{{n_{0}\cos\;\theta_{0}} + {n_{1}\cos\;\theta_{1}}}}} & (1) \\{r_{p} = {\frac{H_{rp}}{H_{ip}} = \frac{{\cos\;{\theta_{0}/n_{0}}} - {\cos\;{\theta_{1}/n_{1}}}}{{\cos\;{\theta/n_{0}}} + {\cos\;{\theta_{0}/n_{1}}}}}} & (2)\end{matrix}$

Meanwhile, when the used wavelength is λ_(i), a refractive index of afilm for the used wavelength is n, a physical thickness of the film isd, and a propagation angle of light in the film is θ, a phase of a waveis expressed by the following expression (3) as a value referred to as aphase thickness Δ.

$\begin{matrix}{\Delta = {\frac{2\pi}{\lambda_{i}}{nd}\mspace{14mu}\cos\;\theta}} & (3)\end{matrix}$

The propagation angles θ₀, θ₁ and θ of light in each film in theexpressions (1) to (3) are calculated from an incident angle θ_(i) ofthe incident light L1 using Snell's law.

As expressed by the expressions (1) and (2), the Fresnel coefficientincreases with an increase of refractive index differences betweenmaterials each configuring the interface. In a general material havingpositive dispersion, dispersion of a material having a high refractiveindex is larger than that of a material having a small refractive index.Thus, shortening a wavelength increases differences between refractiveindexes, in other words, increases the amplitude of a wave. As expressedby the expression (3), the phase thickness Δ varies according to thecoefficient of the refractive index/the wavelength. In a generalmaterial having positive dispersion, the phase thickness Δ increaseswith shortening a wavelength.

As described above, in a material having positive dispersion, theFresnel coefficient r and the phase thickness Δ increases withshortening a wavelength. In other words, varying a wavelength greatlychanges a degree of interference. When a SiO₂ film used in thisembodiment is formed on a grass substrate having a refractive index of1.80, reflectance characteristics and refractive index dispersion arerespectively shown in FIGS. 2 and 3. When the wavelength λ is 550 nm andthe incident angle θ_(i) is 0 degrees, a phase thickness of the SiO₂film is set to be λ/4. In FIGS. 2 and 3, each solid line represents agraph in the case where the SiO₂ film has positive dispersion, eachdotted line represents a graph in the case where the SiO₂ film does nothave positive dispersion, and each dashed-dotted line represents a graphin the case where the SiO₂ film has negative dispersion. The graphs inthe case where the SiO₂ film does not have positive dispersion or in thecase where the SiO₂ film has negative dispersion are calculated using acomputer. As illustrated in FIG. 2, reflectance significantly varies ona short wavelength side in any case, but a variation of reflectance inthe case where the SiO₂ film does not have positive dispersion or in thecase where the SiO₂ film has negative dispersion are suppressed comparedto a variation of reflectance in the case where the SiO₂ has positivedispersion. As just described, characteristics of the interference filmsignificantly varies according to a wavelength, but a variation ofinterference in the film including a general material having positivedispersion becomes larger. In addition, FIG. 4 is a chart illustratingrefractive index dispersion of a Ta₂O₅ film used in this embodiment. TheTa₂O₅ film is transparent at a visible range, and has positivedispersion.

First Example

A material of an interference thin film generally has positivedispersion, and, in principle, it is difficult that a material of aninterference film has negative dispersion. Thus, in this example, amultilayer film having negative dispersion is achieved by setting anappropriate refractive index of each thin film configuring themultilayer film and an appropriate thickness relation using anequivalent film theory that a multilayer film has a function equivalentto a thin film having one layer.

In a film stack 106 according to this example, films 102 to 104 arestacked in order from a substrate 101 side to satisfy the abovecondition. Below, each of the films 102 and 104, and the film 103 areexplained as an H-film and an M-film, respectively. In this example, thefollowing conditional expressions (4) to (6) should be satisfied.

$\begin{matrix}{\frac{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{M}^{2}\tan\;\Delta_{M}} - {U_{H}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}}{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{H}^{2}\tan\;\Delta_{M}} - {U_{M}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}} > 0} & (4) \\{U_{H,M} = {n_{H,M}\cos\;\theta_{H,M}}} & (5) \\{\Delta_{{H,M}\;} = {\frac{2\;\pi}{\lambda_{i}}n_{H,M}d_{H,M}\cos\;\theta_{H,M}}} & (6)\end{matrix}$

Here, θ_(i) is an incident angle of light incident on the multilayerfilm, and λ_(i) is a used wavelength. Additionally, n_(H) is arefractive index of the H-films 102 and 104 for the used wavelengthλ_(i), d_(H) is a physical thickness of the H-films 102 and 104, n_(M)is a refractive index of the M-film 103 for the used wavelength λ_(i),d_(M) is a physical thickness of the M-film 103. The incident angleθ_(i) is, as illustrated in FIG. 1, an angle of light incident on themultilayer film configured by the films 102 to 105 from an incidentmedium.

As illustrated in FIG. 1B, when the film stack 106 is converted into oneequivalent film 200, an equivalent refractive index n_(T) and a physicalthickness d_(T) of the equivalent film 200 are calculated using thefollowing numerical expressions (7) to (11).

$\begin{matrix}{\mspace{79mu}{U_{T}^{2} = {U_{1}^{2}\frac{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{M}^{2}\tan\;\Delta_{M}} - {U_{H}^{2}\tan^{2}\Delta_{H}\;\tan\;\Delta_{M}}}{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{H}^{2}\tan\;\Delta_{M}} - {U_{M}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}}}}} & (7) \\{{\sin\;\Delta_{T}} = {U_{T}( {{\frac{2}{U_{H}}\cos\;\Delta_{H}\sin\;\Delta_{H}\;\cos\;\Delta_{M}} + {\frac{{U_{H}^{2}\cos^{2}\Delta_{H}} - {U_{M}^{2}\sin^{2}\Delta_{H}}}{U_{H}^{2}U_{M}}\sin\;\Delta_{M}}} )}} & (8) \\{{\cos\;\Delta_{T}} = {{\cos^{2}\Delta_{H}\cos\;\Delta_{M}} - {\sin^{2}\Delta_{H}\cos\;\Delta_{M}} - {\frac{U_{H}^{2} + U_{M}^{2}}{U_{H}H_{M}}\cos\;\Delta_{H}\sin\;\Delta_{H}\sin\;\Delta_{M}}}} & (9) \\{\mspace{85mu}{U_{T,H,M} = \{ \begin{matrix}{n_{T,H,M}\cos\;\theta_{T,H,M}} & {S\mspace{14mu}{poralization}} \\\frac{n_{T,H,M}}{\cos\;\theta_{T,H,M}} & {P\mspace{14mu}{poralization}}\end{matrix} }} & (10) \\{\mspace{79mu}{\Delta_{{T,H,M}\;} = {\frac{2\;\pi}{\lambda_{i}}n_{T,H,M}d_{T,H,M}\cos\;\theta_{T,H,M}}}} & (11)\end{matrix}$

The equivalent refractive index n_(T) and the physical thickness d_(T)are calculated by obtaining a symbol U_(T) and a phase thickness Δ_(T)from symbols U_(H,M) and Δ_(H,M) using the above numerical expressions.As the symbol U differs depending on polarization, selecting thenumerical expression according to incident polarization is required. Thephase thickness Δ_(T) may be calculated using the numerical expressions(8) and (9). As each left side of the numerical expressions (8) and (9)is a trigonometric function, using either one of numerical expressions(8) and (9) cannot uniquely determine the phase thickness Δ_(T) within arange of 0 to 360 degrees, but using both of them can derive the phasethickness Δ_(T) within a range of 0 to 360 degrees.

As a left side of the numerical expression (7) is a square value,satisfying the conditional expression (4) over the entire range of aused wavelength range of an optical element 100 is required to enablethe film stack 106 to function as the one equivalent film 200. When theconditional expression (4) is not satisfied, the film stack 106 is notfunctioned as a film having unique characteristics as the equivalentfilm 200, and the H-films 102 and 104, and the M-film 103 havingdifferent properties for each wavelength individually function. Wheneach film individually functions, the film stack 106 cannot havenegative dispersion as the one equivalent film 200. For example, whenthe film stack 106 satisfies the conditional expression (4) over a widewavelength range like a visible range, each film need to select asufficiently thin physical thickness. Moreover, though unintended filmmay be included when forming the H-film and the M-film, such a filmgenerally has an optical thickness smaller than 10 nm and cannotfunction as a film, having no effect on the H-film and the M-film.

Additionally, when d_(HO) is a physical thickness of the H-film 104 onan optical surface side of the outermost layers of the film stack 106and d_(MO) is a physical thickness of the M-film 103 adjacent to theH-film 104, the following conditional expression (12) is preferablysatisfied.n _(HO) d _(HO) +n _(MO) d _(MO)>0.1λ  (12)

In this example, the Ta₂O₅ film is used as the H-films 102 and 104, andthe SiO₂ film is used as the M-film 103. FIG. 8 is a diagramillustrating an equivalent refractive index for a wavelength of 550 nm.FIG. 9 is a diagram illustrating a refractive index of wavelengths of400 to 700 nm. An arrow of FIG. 8 represents a tendency that theequivalent refractive index n_(T) decreases with an increase of thephysical thickness d_(M) of the M-film 103. Furthermore, in FIG. 9, aregion of the film stack 106 that has positive dispersion or fails tosatisfy the expression (1) is filled in black. The Ta₂O₅ film used asthe H-films 102 and 104 has strong positive dispersion and thus the filmstack 106 does not have negative dispersion under a predeterminedcondition, but satisfying the conditional expression (12) allows thefilm stack 106 to approximately have negative dispersion.

Satisfying the following conditional expression (13) at a centralwavelength of the used wavelength range is also preferable.

$\begin{matrix}{{- 0.1} < {{\cos^{2}\Delta_{H}\;\cos\;\Delta_{M}} - {\sin^{2}\Delta_{H}\cos\;\Delta_{M}} - {\frac{U_{H}^{2} + U_{M}^{2}}{U_{H}U_{M}}\cos\;\Delta_{H}\sin\;\Delta_{H}\sin\;\Delta_{M}}} < 0.1} & (13)\end{matrix}$

A center part of the conditional expression (13) is a right side of thenumerical expression (9). In other words, the conditional expression(13) expresses that a cosine of the phase thickness Δ_(T) of the filmstack 106 is near 0. This expresses that the phase thickness Δ_(T) isrepresented as 90[deg]+180[deg]×(arbitrary integer), and is an oddmultiple of λ/4 when expressed using an optical thickness n_(T)×d_(T) ofthe film stack 106. When the optical thickness of the film stack 106 isλ/4, maximum amplitude and a maximum phase variation are observed as theinterference thin film. Such a film stack 106 can be effectively usedfor an optical element such as a dielectric mirror, a dichroic mirrorand an antireflection film.

In this example, the Ta₂O₅ film having the phase thickness of 8.2 nm isused as the H-films 102 and 104, and the SiO₂ film having the phasethickness of 67.0 nm is used as the M-film 103. FIG. 5 is a chartillustrating the equivalent refractive index of the equivalent film 200.FIG. 6 is a chart illustrating the equivalent physical thickness of theequivalent film 200. FIG. 7 is a chart illustrating a calculation resultof the conditional expression (4) when the incident angle θ_(i) is 0degrees and the used wavelength range is a visible range. A designcentral wavelength is a wavelength of 550 nm.

As illustrated in FIG. 7, the calculation result is positive over theentire range of the visible range and thus satisfies the conditionalexpression (4). The center part of the conditional expression (13) isalso 0 at a wavelength of 550 nm and thus satisfies the conditionalexpression (13). Accordingly, as illustrated in FIG. 5, the refractiveindex lowers on a short wavelength side. Moreover, the physicalthickness of the equivalent film 200 varies for a wavelength by a phaseof interference of a wave unlike a general thin film, being required toconsider when designing the equivalent film 200.

FIG. 10 is a chart illustrating reflectance characteristics of adichroic film using the multilayer film according to this example. Asolid line represents a graph of the dichroic film according to thisexample, and a dotted line represents a graph of a multilayer filmaccording to a first comparison example using an YF₃ film havingpositive dispersion. Table 1 provides a film configuration according tothis example, and Table 2 provides a film configuration according to thefirst comparison example.

TABLE 1 Equivalent Equivalent Wave- Physical refractive Physical lengththickness index thickness Film # Film n [nm] n_(T) d_(T) [nm]configuration j1i air 1.000 — — — — j14 Ta₂O₅ 2.209 8.2 1.530 89.9 ×10j13 SiO₂ 1.472 67.0 j12 Ta₂O₅ 2.209 8.2 j11 Ta₂O₅ 2.209 124.5 — — j1sWhite 1.530 — — — — board

TABLE 2 Equivalent Equivalent Wave- Physical refractive Physical Filmlength thickness index thickness con- # Film n [nm] n_(T) d_(T) [nm]figuration h1i air 1.000 — — — — h12 YF3 1.530  89.9 — — ×10 h11 Ta₂O₅2.209 124.5 — — h1s White 1.530 — — — — board

As illustrated in FIG. 10, a range, which is less than or equal to awavelength of 450 nm and is a reflection range of this example, is widerthan that of the first comparison example. Reflectance corresponding toa wavelength, which is greater than or equal to a wavelength of 450 nmand is within a transmission range, also substantially remainsunchanged. Accordingly, using negative dispersion can simply control arange. In general, using positive dispersion easily narrows a range, butrequires a complicated film configuration to widen a range. A method ofthe present invention virtually achieving the multilayer film havingnegative dispersion can be one of countermeasures.

As shown in table 1, the Ta₂O₅ film is used as the H-film (films j12 andj14) of the film stack (films j12 to j14) according to this example. TheTa₂O₅ film is also used for the film j11. In manufacturing of the films,the films j11 and j12 may be formed as the film having the physicalthickness of 132.7 nm at the same time without separately forming them.As just described, when the same material as the film stack havingnegative dispersion is used as a material of a thin film, the physicalthickness may be synthesized.

In this example, the film stack (films j12 to j14) and the film j11 arerepeated ten times. In other words, a stack group, where the film stackis repeated two times, is repeated five times. As described in a secondexample, repeating the film stack two times obtains an equivalent filmhaving an optical thickness of λ/2. When the multilayer film accordingto this example using reflection is used, forming it to include at leastfive stack groups can improve efficiency of reflection. Inmanufacturing, a repeat count is preferably limited to 200 times.

When the multilayer film (films j11 to j14) are used, the opticalthickness and the refractive index of each film need not completelycoincide with each other, and may have a margin within a range not todeviate from the essence of thin film interference. The films having therefractive indexes different by about ±0.02 nm at a design centralwavelength or the optical thicknesses different by a value being equalto or less than 1/20 of the design central wavelength may be regarded ashaving the same interference characteristics.

Second Example

In this example, an optical element 100 includes a multilayer filmhaving an optical thickness n_(T)×d_(T) of λ/2 at a wavelength of 550nm, and thus the multilayer film includes a plurality of film stacks106. When the optical thickness n_(T)×d_(T) is λ/2, a phase thicknessΔ_(T) is 180 degrees. At this time, in the expression (8), as the leftside is 0, that is, the symbol U_(T) is 0, the refractive index cannotbe calculated. In other words, using only one film stack 106 cannotobtain the multilayer film having the optical thickness n_(T)×d_(T) ofλ/2. Accordingly, the multilayer film is configured by a plurality ofequivalent films 200 formed to have the optical thickness n_(T)×d_(T) ofa value equal to or less than λ/4. This can increase a physicalthickness without varying dispersion of a refractive index. As a result,the multilayer film having the optical thickness n_(T)×d_(T) of λ/2 canbe obtained. The number of staking of the equivalent film 200 ispreferably 2 or 3 times. More preferably, as this example, theequivalent film 200 is repeated two times.

In this example, the Ta₂O₅ film having a physical thickness of 25.0 nmis used as H-films 102 and 104 of the film stack 106, and the SiO₂ filmhaving a physical thickness of 17.0 nm is used as an M-film 103 of thefilm stack 106. The film stack 106 is also repeated two times. FIG. 11is a chart illustrating an equivalent refractive index of the equivalentfilm 200. FIG. 12 is a chart illustrating an equivalent physicalthickness of the equivalent film 200. FIG. 13 is a calculation result ofthe conditional expression (4) when an incident angle θ_(i) is 0 degreesand a used wavelength range is a visible range. A design centralwavelength is a wavelength of 550 nm.

As illustrated in FIG. 13, the calculation result is positive over theentire range of the visible range, and thus satisfies the conditionalexpression (4). The center part of the conditional expression (13) isalso 0 at a wavelength of 550 nm and thus satisfies the conditionalexpression (13). Accordingly, as illustrated in FIG. 11, the refractiveindex lowers on a short wavelength side.

FIG. 14 is a chart illustrating reflectance characteristics of anantireflection film using the multilayer film according to this example.A solid line represents a graph of the antireflection film according tothis example, and a dotted line represents a graph of a multilayer filmaccording to a second comparison example. Additionally, the usedwavelength range of the multilayer film according to this example is thevisible range, but, in the figure, reflectance characteristics forwavelengths of 300 to 1000 nm are illustrated. Table 3 provides a filmconfiguration according to this example, and Table 4 provides a filmconfiguration according to the second comparison example.

TABLE 3 Equivalent Equivalent Wave- Physical refractive Physical lengththickness index thickness Film # Film n [nm] n_(T) d_(T) [nm]configuration j2i air 1.000 — — — — j27 MgF₂ 1.476 93.2 — — — j26 Ta₂O₅2.209 25.0 1.966 127.2 ×1 j25 SiO₂ 1.472 17.0 j24 Ta₂O₅ 2.209 25.0 j23Ta₂O₅ 2.209 25.0 j22 SiO₂ 1.472 17.0 j21 Ta₂O₅ 2.209 25.0 j2s White1.530 — — — — board

TABLE 4 Equivalent Equivalent Wave- Physical refractive Physical Filmlength thickness index thickness con- # Film n [nm] n_(T) d_(T) [nm]figuration h2i air 1.000 — — — — h22 MgF₂ 1.476  93.2 — — ×1 h21 ZrO₂₊1.970 139.6 — — Al₂O₅ h2s White 1.530 — — — — board

As shown in table 3, in the multilayer film according to this example,two film stacks (films j21 to j23 and films j24 to j26) are repeatedlystacked. The two film stacks (the films j21 to j23 and the films j24 toj26) serve as one equivalent film. The equivalent refractive index n_(T)and the physical thickness d_(T) are respectively 1.966 and 127.2 nm.

As illustrated in FIG. 14, in a wide band, reflectance of this exampleis lower than that of the second comparison example. Accordingly, usingthe multilayer film according to this example to adjust a phasesignificantly improves efficiency compared to using a film havingpositive dispersion. Reflectance on the short wavelength of theequivalent film according to this example also especially drops. Ingeneral, when an antireflection film is formed using a thin film havinga thickness of λ/2, λ/4 or a value thinner than them for a designcentral wavelength, reflectance on the short wavelength side rarelydrops. This is because that reflection on the short wavelength is addedto light having a peak wavelength. Lowering reflectance on the shortwavelength is difficult, and, to obtain a wide band antireflection filmhaving in a wide band, dropping characteristics on a long wavelengthside is required. Using the multilayer film according to this examplehaving negative dispersion, as illustrated in FIG. 14, improvesreflectance characteristics on the short wavelength and thus can obtaina wide band antireflection film.

Third Example

FIG. 15 is a perspective view of a digital camera as one example of anoptical apparatus using an optical element 100 of the present invention.A digital camera includes a camera body 1600 and an image pickup opticalsystem 1601. The image pickup optical system 1601 may be detachablyattached to the camera body 1600. The camera body 1600 includes a solidimage pickup element (a photoelectric conversion element) 1602 such as aCCD sensor and a CMOS sensor, a memory 1603 and a display 1604. Thesolid image pickup element 1602 is built in the camera body 1600 andreceives an object image formed by the image pickup optical system 1601.The memory 1603 stores information corresponding to the object imagephotoelectrically converted by the solid image pickup element 1602.

The optical element 100 of the present invention is, for example, usedfor an antireflection film formed on a surface of an optical lens of theimage pickup optical system 1601. Thereby, the image pickup opticalsystem 1601 that improve transmittance in wider band can be provided.The optical element of the present invention can be also used for anoptical apparatus including an optical system transmitting light of anapparatus such as a microscope and a projector.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2015-197553, filed on Oct. 5, 2015, which is hereby incorporated byreference herein in its entirety.

What is claimed is:
 1. An optical element that includes an opticalsurface having a multilayer film, wherein the multilayer film comprisesat least two stacks, each of the at least two stacks including a firstfilm having a first refractive index for a light of a wavelength of λiand a second film having a second refractive index for the light smallerthan the first refractive index, wherein outermost layers of each of theat least two stacks, which are a film disposed at a position closest tothe optical surface in each of the at least two stacks and a filmdisposed at a position furthest away from the optical surface in each ofthe at least two stacks, are configured by the first film, wherein afilm configuration of each of the at least two stacks has symmetry alonga stack direction such that each of the at least two stacks consists ofthe first film, the second film, and the first film from the positionfurthest away from the optical surface in each of the at least twostacks to the position closest to the optical surface in each of the atleast two stacks, with the first films in each of the at least twostacks having equivalent physical thicknesses as each other, and whereinthe following conditional expressions are satisfied such that each ofthe at least two stacks functions as one equivalent film having negativedispersion:${\frac{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{M}^{2}\tan\;\Delta_{M}} - {U_{H}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}}{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{H}^{2}\tan\;\Delta_{M}} - {U_{M}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}} > 0},{U_{H} = {n_{H}\cos\mspace{11mu}\theta_{H}}},{U_{M} = {n_{M}\cos\mspace{11mu}\theta_{M}}},{\Delta_{H\;} = {\frac{2\;\pi}{\lambda_{i}}n_{H}d_{H}\cos\;\theta_{H}}},{and}$${\Delta_{M\;} = {\frac{2\;\pi}{\lambda_{i}}n_{M}d_{M}\cos\;\theta_{M}}},$where θ_(H) is a propagation angle of an incident light in the firstfilm, θ_(M) is a propagation angle of the incident light in the secondfilm, n_(H) is the first refractive index, n_(M) is the secondrefractive index, d_(H) is a physical thickness of the first film, andd_(M) is a physical thickness of the second film.
 2. The optical elementaccording to claim 1, wherein the following conditional expression issatisfied:n _(HO) d _(HO) +n _(MO) d _(MO)>0.1λi where d_(HO) is a physicalthickness of the one of the outermost films which is disposed on anoptical surface side, and d_(MO) is a physical thickness of a secondfilm adjacent to the one of the outermost films which is disposed on theoptical surface side.
 3. The optical element according to claim 1,wherein the following conditional expression is satisfied at a centralwavelength of a wavelength range which includes the wavelength of λi andat least either one of a visible range and a near infrared range:${- 0.1} < {{\cos^{2}\Delta_{H}\;\cos\;\Delta_{M}} - {\sin^{2}\Delta_{H}\cos\;\Delta_{M}} - {\frac{U_{H}^{2} + U_{M}^{2}}{U_{H}U_{M}}\cos\;\Delta_{H}\sin\;\Delta_{H}\sin\;\Delta_{M}}} < {0.1.}$4. The optical element according to claim 3, wherein the multilayer filmincludes three stacks.
 5. The optical element according to claim 3,wherein the multilayer film includes at least five stack groups eachhaving the at least two stacks.
 6. An optical apparatus comprising: aplurality of optical elements; wherein at least one of the plurality ofoptical elements includes an optical surface having a multilayer film,wherein the multilayer film comprises at least two stacks, each of theat least two stacks including a first film having a first refractiveindex for a light of a wavelength of λi and a second film having asecond refractive index for the light smaller than the first refractiveindex, wherein outermost layers of each of the at least two stacks,which are a film disposed at a position closest to the optical surfacein each of the at least two stacks and a film disposed at a positionfurthest away from the optical surface in each of the at least twostacks are configured by the first film, wherein a film configuration ofeach of the at least two stacks has symmetry along a stack directionsuch that each of the at least two stacks consists of the first film,the second film, and the first film from the position furthest away fromthe optical surface in each of the at least two stacks to the positionclosest to the optical surface in each of the at least two stacks, withthe first films in each of the at least two stacks having equivalentphysical thicknesses as each other, and wherein the followingconditional expressions are satisfied such that each of the at least twostacks functions as one equivalent film having negative dispersion:${\frac{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{M}^{2}\tan\;\Delta_{M}} - {U_{H}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}}{{2U_{H}U_{M}\tan\;\Delta_{H}} + {U_{H}^{2}\tan\;\Delta_{M}} - {U_{M}^{2}\tan^{2}\Delta_{H}\tan\;\Delta_{M}}} > 0},{U_{H} = {n_{H}\cos\mspace{11mu}\theta_{H}}},{U_{M} = {n_{M}\cos\mspace{11mu}\theta_{M}}},{\Delta_{H\;} = {\frac{2\;\pi}{\lambda_{i}}n_{H}d_{H}\cos\;\theta_{H}}},{and}$${\Delta_{M\;} = {\frac{2\;\pi}{\lambda_{i}}n_{M}d_{M}\cos\;\theta_{M}}},$where θ_(H) is a propagation angle of an incident light in the firstfilm, θ_(M) is a propagation angle of the incident light in the secondfilm, n_(H) is the first refractive index, n_(M) is the secondrefractive index, d_(H) is a physical thickness of the first film, andd_(M) is a physical thickness of the second film.